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qaws [65]
3 years ago
10

Complete the input-output table for log4X. How would I solve this?

Mathematics
1 answer:
vredina [299]3 years ago
5 0

Answer:

x \to f(x)

0.25 \to -1

0.5 \to -0.5

1 \to 0

2 \to 0.5

4 \to 1

8 \to 1.5

Step-by-step explanation:

Given

f(x) = log_4(x)

x = 0.5

f(x) = log_4(x)

f(0.5) = log_4(0.5)

Apply law of logarithm

f(0.5) = \frac{log(0.5)}{log(4)}

Using a calculator, we have:

f(0.5) = -0.5

x = 1

f(x) = log_4(x)

f(1) = log_4(1)

Express 1 as 4^0

f(1) = log_4(4^0)

Apply law of logarithm

f(1) = 0*log_4(4)

f(1) = 0

x = 2

f(x) = log_4(x)

f(2) = log_4(2)

Apply law of logarithm

f(2) = \frac{log(2)}{log(4)}

Using a calculator, we have:

f(2) = 0.5

x = 4

f(x) = log_4(x)

f(4) = log_4(4)

log_a(a) = 1

So:

f(4) = 1

x = 8

f(x) = log_4(x)

f(8) = log_4(8)

Apply law of logarithm

f(8) = \frac{log(8)}{log(4)}

Using a calculator, we have:

f(8) = 1.5

So, the complete table is:

x \to f(x)

0.25 \to -1

0.5 \to -0.5

1 \to 0

2 \to 0.5

4 \to 1

8 \to 1.5

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